A Review on Variation in Band Gap Energy of Quantum Dot with Its Size

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International Journal For Technological Research In Engineering Volume 6, Issue 11, July-2019 ISSN (Online): 2347 - 4718

A REVIEW ON VARIATION IN BAND GAP ENERGY OF QUANTUM DOT WITH ITS SIZE

Kirti Vishwakarma Principal, Gyan Ganga college of Excellence, Jabalpur, India

ABSTRACT: Nanotechnology is the coming revolution in lasers. Quantum-confined semiconductor structures, molecular engineering, and therefore, it is curiosity-driven including quantum wells, quantum rods, and quantum dots, and promising area of technology. The field of nano- have been extensively investigated in the past few years. One science and nanotechnology is interdisciplinary in nature of the most interesting effects of low-dimensional and being studied by physicists, chemists, material semiconductor structures is the size-dependent band gap. [3- scientists, biologists, engineers, computer scientists, etc. 5] The exciton Bohr radius is a threshold value, and the Research in the field of nano-particles has been triggered confinement effect becomes important when the quantum dot by the recent availability of revolutionary instruments and radius is smaller. For small quantum dots, the exciton approaches that allow the investigation of material binding energy and biexciton binding energy (exciton- properties with a resolution close to the atomic level. The exciton interaction energy) is much larger than that for bulk quantum confinement effect is observed when the size of materials. [6]. To understand this effect we break the words the particle is too small to be comparable to the wavelength like quantum and confinement, the word confinement means of the electron. Quantum confinement effect modifies the to confine the motion of randomly moving electron to restrict electronic structure of nano-particles when their sizes its motion in specific energy levels and quantum reflects the become comparable to that of their Bohr excitonic radius. atomic realm of particle. So as the size of a particle decrease When the particle radius falls below the excitonic Bohr till we reach a nano scale the decrease in confining radius, the band gap energy is broadened, leading to a blue dimension makes the energy levels discrete and this shift in the band gap emission spectra, etc. increases or widens up the band gap and ultimately the band KEYWORDS: Nano-particles, quantum dot, Energy band gap energy also increases. The quantum dot is an assembly gap, quantum confinement of atoms of specific material that has few nanometer dimensions. It is termed as a virtual atom. Because of this I. INTRODUCTION microscopic size the electrons are confined inside the dot. The most popular term in the nano world is quantum This is the same for the electrons in an atom they are confinement effect which is essentially due to changes in the confined and localized in the atomic space. In order to obtain atomic structure as a result of direct influence of ultra-small the possible energy levels in the atom or in the dot because length scale on the energy band structure. The length scale of the space confinement one has to use quantum mechanical corresponds to the regime of quantum confinement ranges laws. That is one has to solve the Schrodinger equation with from 1 to 25 nm for typical semiconductor groups of IV, III- relevant boundary condition. The motion of electrons in the V and II-VI. In which the spatial extent of the electronic confined space can be modeled by the motion of a particle in wave function is comparable with the particle size. As a a potential well with infinite walls. While the atom is result of these "geometrical" constraints, electrons "feel" the modeled by one well with infinite wall with size of the atom, presence of the particle boundaries and respond to changes in the electrons in the quantum dot can be modeled by a particle size by adjusting their energy. This phenomenon is potential well with infinite walls with the minimum energy known as the quantum-size effect. Quantization effects level is that of the conduction band. So, the picture is now is become most important when the particle dimension of a that we have electrons confined in the conduction band and semiconductor near to and below the bulk semiconductor holes in the valence band. If there is no confinement as in big Bohr exciton radius which makes materials properties size crystal, there will be no confinement and the electrons in the dependent. conduction band will occupy the bottom of the conduction band and the holes will reside at the top of the valence band. II. REVIEW ON BAND GAP When we solve Schrodinger equation in potential well with Quantum dots are semiconductor nanoparticle whose infinite wall we find that the electrons will have only discrete excitons are confined in all three spatial dimensions. [1] It is energy levels in the valence band. The energy level diagram often called artificial atom because of its quantum properties in the conduction band will be similar to that of an atom and and interactions similar to bulk semiconductor materials. so the energy levels of the holes in the valence band will Generally, the smaller the size of the crystal, the larger the have also discrete energy levels as the shown in the energy band gap energy; the greater the difference in energy between level diagram . [7] the highest valence band and the lowest conduction band becomes, therefore, more energy is needed to excite the dot, and the crystal returns to its ground state. [2] Quantum dot structures are widely used as gain material for semiconductor

below its melting point. In contrast, a material with a large band gap is an insulator. In conductors the valence and conduction bands may overlap, so they may not have a band gap. The conductivity of intrinsic semiconductor is strongly dependent on the band gap. The only available charge carriers for conduction are the electrons that have enough thermal energy to be excited across the band gap and the electron hole that are left off when such an excitation occurs.

The energy levels above the conduction band has an energy measured from the conduction band edge 2 2 2 2 Ene = n h / 8 π me d , Where h is the Planck constant, n the order of the level, me is the effective mass of electrons in the quantum dot and d is the width of the dot. The same equation holds for the holes energy Enh in the valence band with mh the hole effective mass instead of me. So, the energy gap for the quantum dot becomes qd Eg = Eg + E1e + E1h, E1e is the excess energy of the first level in the quantum dot and E1h is that corresponding level for the holes. It is clear that one can tune the effective energy gap in the quantum dot by changing its size d.

When the separation of two confining surfaces is less than de broglie wavelength of the electron then electron energy is III. CONCLUSIONS quantized which is the 2D quantum confinement effect. Such Electronic states of an atom are typically characterized by a confinement can be realized in 3-D leading to quantum box discrete energy levels that are often separated by electron or dot. The physical properties of a quantum dot are not volts. The band gap energy of the quantum dot increases affected quantum confinement; however, their optical with the reduction of its size because of the quantum absorption and emission can be tuned via the quantum size confinement The spatial distribution of these states is highly effect. A useful model for this is the particle in a sphere. localized. At the nanoscale, the dimension of energy states In metals and semiconductors the electronic wave functions resides between these limits. In the nanoscale phenomena, of conduction electrons are delocalized over the entire the energy level spacing of electronic states of atom particle. These electrons can, therefore, be described increases with reduction in dimensionality of particle and is qualitatively as particles in a dot. Thus the densities of states called Quantum Confinement. The QC phenomena can be and the energies of the particles depend crucially on the size readily understood from the well-known Heisenberg‟s of the dot which leads to some extent to a smooth size uncertainty principle. Since the uncertainty in momentum dependence. E.g. ionization energies and electron affinities cannot exceed the momentum. If one tries to localize the are tuned between the atomic values and the work function of position of an electron by reducing the box size, its energy the bulk material by variation of the cluster size. However, must increases and diverges as the confining region vanishes. there are also discontinuities which are due to filled shell Hence, depending on the dimensions in which the length structures leading e.g. to extra stability of such clusters scale is nanometers, they can be classified into: (a) („pseudo-atoms‟). nanoparticles (0-D), (b) lamellar structure (1-D), (c) The variation of nanoparticle size generates novel properties filamentary structure (2-D), and (d) bulk nanostructured (3- that can hardly be seen in the bulk, such as the conduction- D) materials. The densities of states and the energies of the insulator and nonmagnetic-magnetic transition of noble particles depend crucially on the size of the dot which leads metals (e.g. Au at ~2-3nm) at the nanoscale. We know that to some extent to a smooth size dependence. one electron energy level of atoms is split into two levels, when a two-atom molecule is formed. With an increase in the REFERENCES number of atoms in the nanoparticle, the energy level [1] M. A. Reed, E. S. Hornbeck,et.al., “Quantum Dots,” continues to split and finally, merge into quasi–continuous Scientific American, 268, 1, 118-123 (1993). band structure in the bulk solid. However, for small particles [2] R. D Schaller and V. I. Klimov, Physical Review with dimension in the nanometer regime, the electron states Letters, 92, 18 (2004) are not continuous but discrete, due to the confinement of the [3] E.O. Chukwuocha, M.C. Onyeaju and T. T. Harry, electron wave function. A semiconductor is a material with World Journal of Condensed Matter Physics, 2, 96- an intermediate sized but non-zero band gap that behaves as 100, (2012). an insulator at absolute zero but allows thermal excitation of [4] H. Yu, J. Li, R. A. Loomis, P. C. Gibbons, L. W. electrons into its conduction band at temperatures that are Wang and W. E. Buhro, J. Am. Chem. Soc., 125,

16168, (2003). [5] L. L. Li, J. Hu, W. Yang and A. P. Alivisatos, Nano Lett., 1, 349, (2001). [6] V.I. Klimov, J. Phys. Chem. B, 110, 16827–16845 (2006). [7] L.E.Brus, J. Chem. Phys., 79, 5566–5571 (1983).